Gather Analysis
Barrasso Marco
2024-02-17
Gather Analysis
Mapped by core
library(ggplot2)
library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(tidyr)
library(dbplyr)##
## Attaching package: 'dbplyr'## The following objects are masked from 'package:dplyr':
##
## ident, sqlgather_core_thin = read.csv("~/Downloads/hpc_ex1/thin/gather_core_thin.csv")
gather_core_plot = gather_core_thin %>%
pivot_longer(cols = c(basic_linear, binomial)) %>%
ggplot(aes(x = cores, y = value, color = name)) +
geom_vline(xintercept = c(12,24), linetype = "dashed", color = "black")+
annotate("text", x = c(12,24), y = rep(0,2), label = c(12,24),
vjust = 1, hjust = -0.1,color="black")+
geom_point(size = 1.5) +
geom_line(aes(group = name), size = 0.6) +
labs(title = "Latency vs # Cores, Mapped by Core, Message Size 1 MPI_CHAR",
x = "# Cores",
y = "Latency (us)",
color = "Allocation") +
theme_bw() +
theme(legend.position = c(0.13, 0.82),
legend.background = element_rect(fill = "transparent", colour = NA))## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.gather_core_plot
Mapped by socket
gather_socket_thin = read.csv("~/Downloads/hpc_ex1/thin/gather_socket_thin.csv")
gather_socket_plot = gather_socket_thin %>%
pivot_longer(cols = c(basic_linear, binomial)) %>%
ggplot(aes(x = cores, y = value, color = name)) +
geom_vline(xintercept = c(12,24), linetype = "dashed", color = "black")+
annotate("text", x = c(12,24), y = rep(0,2), label = c(12,24),
vjust = 1, hjust = -0.1,color="black")+
geom_point(size = 1.5) +
geom_line(aes(group = name), size = 0.6) +
labs(title = "Latency vs # Cores, Mapped by Socket, Message Size 1 MPI_CHAR",
x = "# Cores",
y = "Latency (us)",
color = "Allocation") +
theme_bw() +
theme(legend.position = c(0.13, 0.82),
legend.background = element_rect(fill = "transparent", colour = NA))
gather_socket_plot
Mapped by node
gather_node_thin = read.csv("~/Downloads/hpc_ex1/thin/gather_node_thin.csv")
gather_node_plot = gather_node_thin %>%
pivot_longer(cols = c(basic_linear, binomial)) %>%
ggplot(aes(x = cores, y = value, color = name)) +
geom_vline(xintercept = c(12,24), linetype = "dashed", color = "black")+
annotate("text", x = c(12,24), y = rep(0,2), label = c(12,24),
vjust = 1, hjust = -0.1,color="black")+
geom_point(size = 1.5) +
geom_line(aes(group = name), size = 0.6) +
labs(title = "Latency vs # Cores, Mapped by Node, Message Size 1 MPI_CHAR",
x = "# Cores",
y = "Latency (us)",
color = "Allocation") +
theme_bw() +
ylim(0, 2.1) +
theme(legend.position = c(0.12, 0.86),
legend.background = element_rect(fill = "transparent", colour = NA))
gather_node_plot
Binomial Comparison
binomial = data.frame(core = gather_core_thin$binomial, socket = gather_socket_thin$binomial, node = gather_node_thin$binomial, cores = gather_core_thin$cores)
binomial_plot = binomial %>%
pivot_longer(cols = c(core, socket, node)) %>%
ggplot(aes(x = cores, y = value, color = name)) +
geom_vline(xintercept = c(12,24), linetype = "dashed", color = "black")+
annotate("text", x = c(12,24), y = rep(0,2), label = c(12,24),
vjust = 1, hjust = -0.1,color="black")+
geom_point(size = 1.5) +
geom_line(aes(group = name), size = 0.6) +
labs(title = "Binomial Tree Algorithm, Latency vs # Cores",
x = "# Cores",
y = "Latency (us)",
color = "Allocation") +
theme_bw() +
ylim(0, 2) +
theme(legend.position = c(0.08, 0.84),
legend.background = element_rect(fill = "transparent", colour = NA))
binomial_plot
Gather Performance Model
library(plotly)##
## Attaching package: 'plotly'## The following object is masked from 'package:ggplot2':
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## last_plot## The following object is masked from 'package:stats':
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## filter## The following object is masked from 'package:graphics':
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## layoutbinomial_all = read.csv("~/Downloads/hpc_ex1/thin/gather_binomial.csv")
binomial_all = data.frame(
log2Latency=as.numeric(unlist(log2(binomial_all %>% filter(Allocation == "node") %>% select(Latency)))),
Processes= as.numeric(unlist(binomial_all %>% filter(Allocation == "node") %>% select(Processes))),
log2MessageSize=as.numeric(unlist(log2(binomial_all %>% filter(Allocation == "node") %>% select(MessageSize))))
)
fig <- binomial_all %>%
plot_ly(
x = ~log2MessageSize,
y = ~Processes,
z = ~log2Latency,
type = 'scatter3d',
mode = 'markers',
marker = list(
size = 8,
color = ~log2Latency,
line = list(color = 'black', width = 0.5)
)
) %>%
layout(
scene = list(
xaxis = list(
title = "log2(MessageSize)",
titlefont = list(size = 11)
),
yaxis = list(
title = "Cores",
titlefont = list(size = 11)
),
zaxis = list(
title = "log2(Latency)",
titlefont = list(size = 11)
)
)
)
figbinomial_model = lm(log2Latency ~ -1 + log2MessageSize + Processes + I(log2MessageSize^2), data = binomial_all)
summary(binomial_model)##
## Call:
## lm(formula = log2Latency ~ -1 + log2MessageSize + Processes +
## I(log2MessageSize^2), data = binomial_all)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.85787 -0.22979 0.03264 0.36357 1.45789
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## log2MessageSize -0.3175077 0.0084104 -37.75 <2e-16 ***
## Processes 0.0394438 0.0011324 34.83 <2e-16 ***
## I(log2MessageSize^2) 0.0402835 0.0004586 87.84 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5819 on 984 degrees of freedom
## Multiple R-squared: 0.9847, Adjusted R-squared: 0.9847
## F-statistic: 2.114e+04 on 3 and 984 DF, p-value: < 2.2e-16fig <- binomial_all %>%
plot_ly(
x = ~log2MessageSize,
y = ~Processes,
z = ~log2Latency,
type = 'scatter3d',
mode = 'markers',
marker = list(
size = 6,
color = 'grey',
opacity = 0.3,
line = list(color = 'black', width = 0.5)
)
) %>%
layout(
title = "",
scene = list(
xaxis = list(
title = "log2(MessageSize)",
titlefont = list(size = 11)
),
yaxis = list(
title = "Cores",
titlefont = list(size = 11)
),
zaxis = list(
title = "log2(Latency)",
titlefont = list(size = 11)
)
)
)
x_values <- seq(min(binomial_all$log2MessageSize), max(binomial_all$log2MessageSize), length.out = 100)
y_values <- seq(min(binomial_all$Processes), max(binomial_all$Processes), length.out = 100)
meshgrid <- expand.grid(log2MessageSize = x_values, Processes = y_values)
# Predict the z values using the linear model
z_values <- predict(binomial_model, newdata = meshgrid)
# Reshape the predicted z values into a matrix
z_matrix <- matrix(z_values, nrow = length(y_values), ncol = length(x_values), byrow = TRUE)
fig <- fig %>%
add_surface(
x = ~x_values,
y = ~y_values,
z = z_matrix,
opacity = 1,
colorscale = 'Plasma',
name = 'Regression Plane',
showlegend = FALSE,
showscale = FALSE
)
fig## Warning: 'surface' objects don't have these attributes: 'mode', 'marker'
## Valid attributes include:
## '_deprecated', 'autocolorscale', 'cauto', 'cmax', 'cmid', 'cmin', 'coloraxis', 'colorbar', 'colorscale', 'connectgaps', 'contours', 'customdata', 'customdatasrc', 'hidesurface', 'hoverinfo', 'hoverinfosrc', 'hoverlabel', 'hovertemplate', 'hovertemplatesrc', 'hovertext', 'hovertextsrc', 'ids', 'idssrc', 'legendgroup', 'legendgrouptitle', 'legendrank', 'lighting', 'lightposition', 'meta', 'metasrc', 'name', 'opacity', 'opacityscale', 'reversescale', 'scene', 'showlegend', 'showscale', 'stream', 'surfacecolor', 'surfacecolorsrc', 'text', 'textsrc', 'type', 'uid', 'uirevision', 'visible', 'x', 'xcalendar', 'xhoverformat', 'xsrc', 'y', 'ycalendar', 'yhoverformat', 'ysrc', 'z', 'zcalendar', 'zhoverformat', 'zsrc', 'key', 'set', 'frame', 'transforms', '_isNestedKey', '_isSimpleKey', '_isGraticule', '_bbox'